Selection of recurrence threshold for signal detection

Over the last years recurrence plots (RPs) and recurrence quantification analysis (RQA) have become quite popular in various branches of science. One key problem in applying RPs and RQA is the selection of suitable parameters for the data under investigation. Whereas various well-established methods for the selection of embedding parameters exists, the question of choosing an appropriate threshold has not yet been answered satisfactorily. The recommendations found in the literature are rather rules of thumb than actual guidelines. In this paper we address the issue of threshold selection in RP/RQA. The core criterion for choosing a threshold is the power in signal detection that threshold yields. We will validate our approach by applying it to model as well as real-life data.